In Singularity theory, we often assume there is no limit to the growth of intelligence. That may not be an accurate assumption. While we cannot currently define a limiting factor, it is possible that the growth of intelligence approximates a hyperbolic curve that approaches an asymptote but never crosses it.

We reached the assumption of no limit because we can observe the scaling of intelligence upward as more resources are applied to the process of computation. We don’t see any obvious decay in the upward scaling, but we are only looking at one part of the curve. Hyperbolic curves usually start out with a somewhat steady increase on one axis as the coordinate for the other axis grows. But then the curve changes, bending upward and the scaling ratio between the two axes changes dramatically, even creating a barrier-like asymptote that may never be reached.

A parallel to that in the growth of intelligence might be that at lower points in the growth curve, the scaling is steady. This means as we apply more computational power and memory storage, our measure of intelligence also grows at a predictable rate. But it’s possible that while this growth might continue, it takes ever increasing amounts of resources being added to produce ever shrinking amounts of growth in intelligence. This could result in a point where it takes a huge increase of resources to produce a tiny increase in intelligence and we simply decide the return is no longer worthwhile.